Question

A sample of gas with $\gamma =1.5$ is taken through an adiabiatic process in which the volume is compressed from $1200{\text{cm}}^3$ to $300{\text{cm}}^3$. if the initial pressure is $200\text{kPa}$. The absolute value of the workdone by the gas in the process
$\text{J}$.

• A. 480.00
• B. 480
• C. 480.0

Answer 1

Answer: (A), (B), (C)

For an adiabatic process between two thermodynamic states,
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
Here $P_1=200\text{kPa},V_1=1200{\text{cm}}^3,V_2=300{\text{cm}}^3,\gamma =1.5$

$P_2=200(4{)}^{1.5}=1600\text{kPa}$

Work done by the gas in this adiabatic process is $\frac{P_1{V}_1-P_2{V}_2}{\gamma -1}=\frac{1600\left(300\right)-1200\left(200\right)}{1.5-1}=480\times {10}^6\times {10}^{-6}\text{J}=480\text{J}$

Ans: $480,480.0,480.00$