If 100 L gas is enclosed in a cylinder, absorbs 302.6 J of heat and expands to 200 L against constant…
If 100 L gas is enclosed in a cylinder, absorbs 302.6 J of heat and expands to 200 L against constant external pressure of 2 pascal. Calculate internal energy change of the gas.
200 J
300 J
400 J
100 J
Solution
Given:
- $q=302.6 \mathrm{~J}$,
- External pressure: $P_{\text {ext }}=2 \mathrm{~pascal}$,
- Initial volume: $V_1=100 \mathrm{~L}$,
- Final volume: $V_2=200 \mathrm{~L}$,
- Work done: $W=-P_{\mathrm{ext}} \Delta V$. Step 1: Calculate Work Done ($W$):
$W=-P_{\text {ext }}\left(V_2-V_1\right)=-(2)(200-100)=-200 \mathrm{~J}$ Step 2: Use First Law of Thermodynamics:
$\Delta U=q+W=302.6-200=-102.6 \mathrm{~J} .$ Answer: 100 J, Option 4.