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Heat and TheromdynamicsQuestion and Answers: Page 2

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Derive the expression for the pressure exerted by an ideal gas on the wall of container

$${Derive}\:{the}\:{expression} \\ $$$${for}\:{the}\:{pressure}\:{exerted} \\ $$$${by}\:{an}\:{ideal}\:{gas}\:{on}\:{the} \\ $$$${wall}\:{of}\:{container} \\ $$

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the molar heat capacity of constant pressure of a gas varies with the temperature according to the equation n c_(p=a+bθ−c/θ^(2 _ ) ) where a.b and c are constant how much heat transfered during an isobaric process in which n makes of gas undergo a temperature rise from θ_i to θ_f ? (b)the molar heat capacity of a metal at low temperature varies with the temperature according to the equation c=bθ+(a/h)θ^3 where a and b are constant .how much heat p_(γ ) make is transfered during a process in which the tempereture change from 0.01(h)to 0.02(h)

$${the}\:{molar}\:{heat}\:{capacity}\:{of}\:{constant} \\ $$$${pressure}\:{of}\:{a}\:{gas}\:{varies}\:{with}\:{the} \\ $$$${temperature}\:{according}\:{to}\:{the}\:{equation} \\ $$$${n}\:{c}_{{p}={a}+{b}\theta−{c}/\theta^{\mathrm{2}\:\:\:\:\:\:\underset{} {\:}} } \\ $$$${where}\:{a}.{b}\:{and}\:{c}\:{are}\:{constant}\:{how}\:{much}\:{heat}\:{transfered}\:{during}\:{an}\:{isobaric}\:{process}\:{in}\:{which}\:{n}\:{makes}\:{of}\:{gas}\:{undergo}\:{a}\:{temperature}\:{rise}\:{from}\:\theta_{{i}} \:\:{to}\:\theta_{{f}} \:? \\ $$$$\left({b}\right){the}\:{molar}\:{heat}\:{capacity}\:{of}\:{a}\:{metal}\:{at}\:{low}\:{temperature}\:{varies}\:{with}\:{the}\:{temperature}\:{according}\:{to}\:{the}\:{equation}\:{c}={b}\theta+\frac{{a}}{{h}}\theta^{\mathrm{3}} \:\:{where}\:{a}\:{and}\:{b}\:{are}\:{constant}\:.{how}\:{much}\:{heat}\:{p}_{\gamma\:\:} \:\:{make}\:{is}\:{transfered}\:{during}\:{a}\:{process}\:{in}\:{which}\:{the}\:{tempereture}\:{change}\:{from}\:\mathrm{0}.\mathrm{01}\left({h}\right){to}\:\mathrm{0}.\mathrm{02}\left({h}\right) \\ $$

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A small body with temperature θ and absorbtivity τ is placed in a large evaluated capacity whose interior walls are at a temperature θ_w . when θ_w −θ is small, show that the rate of heat transfer by radiation is Q^• = 4θ_w ^3 Aτδ(θ_w −θ).

$$\mathrm{A}\:\mathrm{small}\:\mathrm{body}\:\mathrm{with}\:\mathrm{temperature}\:\theta\:\mathrm{and} \\ $$$$\mathrm{absorbtivity}\:\tau\:\mathrm{is}\:\mathrm{placed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{large}\: \\ $$$$\mathrm{evaluated}\:\mathrm{capacity}\:\mathrm{whose}\:\mathrm{interior}\: \\ $$$$\mathrm{walls}\:\mathrm{are}\:\mathrm{at}\:\mathrm{a}\:\mathrm{temperature}\:\theta_{\mathrm{w}} . \\ $$$$\mathrm{when}\:\:\:\:\theta_{\mathrm{w}} −\theta\:\:\:\:\mathrm{is}\:\:\mathrm{small},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{rate}\:\mathrm{of}\:\mathrm{heat}\:\mathrm{transfer}\:\mathrm{by}\:\mathrm{radiation}\:\mathrm{is} \\ $$$$\:\:\:\:\:\overset{\bullet} {\mathrm{Q}}=\:\mathrm{4}\theta_{\mathrm{w}} ^{\mathrm{3}} \mathrm{A}\tau\delta\left(\theta_{\mathrm{w}} −\theta\right). \\ $$

Question Number 58216 Answers: 1 Comments: 1

The molar heat capacity of a metal at low temperature varies with the temperature according to the equation C = bθ + (a/H)θ^3 where a, b and H are constant. How much heat per mole is transfered during the process in which the temperature change from 0.01H to 0.02H ?

$$\mathrm{The}\:\mathrm{molar}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{of}\:\mathrm{a}\:\mathrm{metal}\:\:\mathrm{at} \\ $$$$\mathrm{low}\:\mathrm{temperature}\:\mathrm{varies}\:\mathrm{with}\:\mathrm{the}\: \\ $$$$\mathrm{temperature}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\:\:\mathrm{C}\:=\:\mathrm{b}\theta\:+\:\frac{\mathrm{a}}{\mathrm{H}}\theta^{\mathrm{3}} \\ $$$$\mathrm{where}\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{H}\:\mathrm{are}\:\mathrm{constant}. \\ $$$$\mathrm{How}\:\mathrm{much}\:\mathrm{heat}\:\mathrm{per}\:\mathrm{mole}\:\mathrm{is}\:\mathrm{transfered} \\ $$$$\mathrm{during}\:\mathrm{the}\:\mathrm{process}\:\mathrm{in}\:\mathrm{which}\:\mathrm{the}\: \\ $$$$\mathrm{temperature}\:\mathrm{change}\:\mathrm{from}\:\mathrm{0}.\mathrm{01H}\: \\ $$$$\mathrm{to}\:\mathrm{0}.\mathrm{02H}\:? \\ $$

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The molar heat capacity of constant presure of a gas varies with the temperature according to the equation C_p = a + bθ −(C/θ^2 ) where a,b and C are constants. How much heat is transfered during an isobaric process in which n mole of gas undergo a temperature rise from θ_(i ) to θ_f ?

$$\mathrm{The}\:\mathrm{molar}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{of}\:\mathrm{constant} \\ $$$$\mathrm{presure}\:\mathrm{of}\:\mathrm{a}\:\mathrm{gas}\:\mathrm{varies}\:\mathrm{with}\:\mathrm{the}\:\mathrm{temperature} \\ $$$$\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{C}_{\mathrm{p}} \:=\:\:\mathrm{a}\:+\:\mathrm{b}\theta\:−\frac{\mathrm{C}}{\theta^{\mathrm{2}} } \\ $$$$\mathrm{where}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{constants}. \\ $$$$\:\:\mathrm{How}\:\mathrm{much}\:\mathrm{heat}\:\mathrm{is}\:\mathrm{transfered}\:\mathrm{during} \\ $$$$\:\:\:\mathrm{an}\:\mathrm{isobaric}\:\mathrm{process}\:\mathrm{in}\:\mathrm{which}\:\mathrm{n}\:\mathrm{mole} \\ $$$$\:\:\:\mathrm{of}\:\mathrm{gas}\:\mathrm{undergo}\:\mathrm{a}\:\mathrm{temperature}\:\mathrm{rise} \\ $$$$\:\:\:\:\mathrm{from}\:\theta_{{i}\:} \mathrm{to}\:\theta_{{f}} \:? \\ $$

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Two carnot emgines A and B are operated in series. engine A receiepved heat?from a reservoir at 600 K and rejects it to a reservoir at temp T. B receives heat rejected by A and in turn rejects it to reservoir at 100K. Find (η_B /η_A ) η efficiency

$$\mathrm{Two}\:\mathrm{carnot}\:\mathrm{emgines}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{operated}\:\mathrm{in} \\ $$$$\mathrm{series}.\:\mathrm{engine}\:\mathrm{A}\:\mathrm{receiepved}\:\mathrm{heat}?\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{reservoir}\:\mathrm{at}\:\mathrm{600}\:\mathrm{K}\:\mathrm{and}\:\mathrm{rejects}\:\mathrm{it}\:\mathrm{to} \\ $$$$\mathrm{a}\:\mathrm{reservoir}\:\mathrm{at}\:\mathrm{temp}\:\mathrm{T}.\:\mathrm{B}\:\mathrm{receives} \\ $$$$\mathrm{heat}\:\mathrm{rejected}\:\mathrm{by}\:\mathrm{A}\:\mathrm{and}\:\mathrm{in}\:\mathrm{turn}\:\mathrm{rejects} \\ $$$$\mathrm{it}\:\mathrm{to}\:\mathrm{reservoir}\:\mathrm{at}\:\mathrm{100K}. \\ $$$$\mathrm{Find}\:\frac{\eta_{{B}} }{\eta_{{A}} } \\ $$$$\eta\:\mathrm{efficiency} \\ $$

Question Number 51148 Answers: 1 Comments: 0

Two hot cubes are at same temperature and both are cooled by forced convetion the cube are made from the same material but one has side of L metre and other one 2L metre. which cube is at quicker rate of cooling

$${Two}\:{hot}\:{cubes}\:{are}\:\:{at}\:{same}\: \\ $$$${temperature}\:{and} \\ $$$${both}\:{are}\:{cooled}\:{by}\:{forced}\: \\ $$$${convetion}\:{the}\:{cube}\:{are}\:{made} \\ $$$${from}\:{the}\:{same}\:{material} \\ $$$${but}\:{one}\:{has}\:{side}\:{of}\:{L}\:{metre} \\ $$$${and}\:{other}\:{one}\:\mathrm{2}{L}\:{metre}. \\ $$$${which}\:{cube}\:{is}\:{at}\:{quicker}\: \\ $$$${rate}\:{of}\:{cooling} \\ $$$$ \\ $$

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Two similar spherical bodies of radius R and 2R are initially are at same temperature.if they are kept to cool under the same condition.show qualitatively which of the two spherical body will cool faster.

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∅=0

$$\varnothing=\mathrm{0} \\ $$

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During random motion, gas molecules do not interact with each other . Hence Potential energy =0 ...... Pls explain why P.E = 0? P.E is stored form of energy,right?

$${During}\:{random}\:{motion},\:{gas}\:{molecules} \\ $$$${do}\:{not}\:{interact}\:{with}\:{each}\:{other}\:. \\ $$$${Hence}\:\:{Potential}\:{energy}\:=\mathrm{0}\:...... \\ $$$${Pls}\:{explain}\:{why}\:{P}.{E}\:=\:\mathrm{0}? \\ $$$${P}.{E}\:{is}\:{stored}\:{form}\:{of}\:{energy},{right}? \\ $$

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α_1 and α_2 are the temperature coefficients of the two resistors R_1 and R_2 at any temperature T_0 0°C.Find the equivalent resistance if both R_1 and R_(2 ) are connected in series combination.Assume that α_1 and α_2 remain same with change in temperature.

$$\alpha_{\mathrm{1}} \:{and}\:\alpha_{\mathrm{2}} \:{are}\:{the}\:{temperature} \\ $$$${coefficients}\:{of}\:{the}\:{two}\:{resistors} \\ $$$${R}_{\mathrm{1}} \:{and}\:{R}_{\mathrm{2}} \:{at}\:{any}\:{temperature}\:{T}_{\mathrm{0}} \\ $$$$\mathrm{0}°{C}.{Find}\:{the}\:{equivalent}\:{resistance} \\ $$$${if}\:{both}\:{R}_{\mathrm{1}} \:{and}\:{R}_{\mathrm{2}\:} \:{are}\:{connected}\:{in} \\ $$$${series}\:{combination}.{Assume}\:{that} \\ $$$$\alpha_{\mathrm{1}} \:{and}\:\alpha_{\mathrm{2}} \:{remain}\:{same}\:{with}\:{change} \\ $$$${in}\:{temperature}. \\ $$

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