Question

One cubic meter of an ideal gas is at a pressure of ${10}^{5}N/m^2$ and temperature $300K$. The gas is allowed to expand at constant pressure to twice its volume by supplying heat. If the change in internal energy in this process is ${10}^{4}J$, then the heat supplied is

• A. ${10}^{5}J$
• B. ${10}^{4}J$
• C. $11\times {10}^{4}J$
• D. $2.2\times {10}^{5}J$

Answer 1

The correct option is C $11\times {10}^{4}J$

Solution:

$PV=nTR$

$\Rightarrow 10{\times }^5\times 1=n\left(83.14\right)\times 300$

$\Rightarrow n=\frac{{10}^5}{(83.14+300)}$

$\therefore n=40$

change in internal energy is given as ${10}^4$ Joule

$\Rightarrow du={10}^4{=}^n{C}_{V}dT$

[pressure is constant so,$v\alpha T{v}_1=v$ and $v_2=2v$ so, $T_1=300k{T}_2=600k$

Now, Heat supplied$=d\theta {=}^n{C}_{p}dT$

$=n(C_v+R)dT$

$=40(8.21+0.833)\times (600-300)$

$=40\left(9.043\right)\times 300$

$=110000j$

$=11\times {10}^{4}j$

Correct option is (C)