Question

A sample of ideal gas $(\gamma =1.4)$ is heated at constant pressure. If an amount $140$J of heat is supplied to the gas, find
a) the change in internal energy of the gas
b) the work done by the gas.

Answer 1

Solution:-

As the heat is supplied to the system.

Therefore,

$q=140J$

$\gamma =1.4\left(\text{Given}\right)$

As we know that,

$\Delta U=n{C}_{v}dT$

$\Rightarrow \Delta U=\frac{C_v}{C_p}\times \left(C_{p}ndT\right)$

$\Rightarrow \Delta U=\frac{1}{\gamma }\times q(\because \frac{C_p}{C_v}=\gamma \text{and}q=n{C}_{p}dT)$

$\therefore \Delta U=\frac{q}{\gamma }=\frac{140}{1.4}=100J$

Hence the change in internl energy of the gas is $100J$

Now from first law of thermodynamics,

$\Delta U=q+w$

$\Rightarrow w=\Delta U-q$

$\Rightarrow w=100-140=-40J$

Here $-ve$ sign indicates that work is done by the gas.

Hence the work done by the gas is $40J$.