Question

An ideal gas with adiabatic exponent equal to 1.5 undergoes a process in which work done by the gas is same as increase in internal energy of the gas. The total heat given to the gas is

• A. C = 4 r
• B. C = zero
• C. C = 2 r
• D. C = r

Answer 1

The correct option is A C = 4 r

Given: $W=dU$ , adiabatic exponent ($\gamma$)=1.5

Solution:

As $W=dU$ $\to \left(1\right)$

$\Rightarrow \int PdV=\int n{C}_{v}dT$

From first law of thermodynamics, $dQ=dU+W$ $\to \left(2\right)$

Putting value of equation (1) in equation (2) we get,

$\Rightarrow dQ=2dU$

$\Rightarrow nCdT=2n{C}_{v}dT$

$\Rightarrow C=2C_v$

$\Rightarrow C=\frac{2R}{\gamma -1}$

Putting $\gamma =1.5$, we get,

$C=4R$

Hence correct option is A.