One mole of a gas expands such that its volum | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the relation $V = K T^2$.Using the ideal gas equation $PV = RT$ for one mole of gas,we have $P = \frac{RT}{V}$.Substituting $V = K T^2$ into

Vedclass · Accepted Answer

$120 R$

Vedclass · Answer

(D) Given the relation $V = K T^2$.Using the ideal gas equation $PV = RT$ for one mole of gas,we have $P = \frac{RT}{V}$.Substituting $V = K T^2$ into the expression for $P$,we get $P = \frac{RT}{K T^2} = \frac{R}{KT}$.The work done $W$ is given by $W = \int P dV$.Since $V = K T^2$,differentiating with respect to $T$ gives $dV = 2KT dT$.Substituting $P$ and $dV$ into the work integral:$W = \int_{T_1}^{T_2} \left( \frac{R}{KT} ight) (2KT dT) = \int_{T_1}^{T_2} 2R dT$.Given the change in temperature $\Delta T = T_2 - T_1 = 60 	ext{ K}$.Therefore,$W = 2R (T_2 - T_1) = 2R(60) = 120R$.

One mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).

Similar Questions

$A$ container is filled with $20$ moles of an ideal diatomic gas at absolute temperature $T$. When heat is supplied to the gas,the temperature remains constant,but $8$ moles dissociate into atoms. The heat energy given to the gas is ......... (in $R T$)

The temperature-entropy $(T-S)$ diagram of a reversible engine cycle is given in the figure. Its efficiency is

If $R$ is the universal gas constant,the amount of heat needed to raise the temperature of $2$ moles of an ideal monoatomic gas from $273 \ K$ to $373 \ K$ when no work is done is equal to ...... $R$.

$A$ thermodynamic cycle takes in heat energy at a high temperature and rejects energy at a lower temperature. If the amount of energy rejected at the low temperature is $3$ times the amount of work done by the cycle,the efficiency of the cycle is

$A$ gas follows $VT^2 = \text{constant}$. The coefficient of volume expansion of the gas is

Vedclass Test Series

Exam Paper Generator

Online Exam Module