Question

In a thermodynamic process helium gas obeys the law ${\text{TP}}^{\frac{-2}{5}}=\text{constant}$. If temperature of 2 moles of the gas is raised from T to 3T, then

• A. Heat given to the gas is 9RT
• B. Heat given to the gas is zero
• C. Increase in internal energy is 6RT
• D. Work done by the gas is - 6RT

Answer 1

Answer: (B), (C), (D)

The correct options are
B

Heat given to the gas is zero

C

Increase in internal energy is 6RT

D

Work done by the gas is - 6RT

${\text{TP}}^{\frac{-2}{5}}=\text{constant}$

$\therefore \left(\text{PV}\right){\text{P}}^{\frac{-2}{5}}=\text{constant}$

or ${\text{PV}}^{\frac{5}{3}}=\text{constant}$

Comparing with the equation,

${\text{PV}}^x=\text{constant}$

We have $x=\frac{5}{3}$

Molar heat capacity of equation (1) is given by

$\text{C}={\text{C}}_v+\frac{\text{R}}{1-x}$

$=\frac{3}{2}\text{R}+\frac{\text{R}}{1-\frac{5}{3}}=0$

$\therefore \text{Q}=\text{nC}\Delta \text{T}=0$

$\Delta \text{U}=-\text{W}$

$={\text{nC}}_v\Delta \text{T}$

$=\left(2\right)\left(\frac{3}{2}\text{R}\right)(3\text{T}-\text{T})$

$=6\text{RT}$