Question

10 moles of an idal gas expand isothermally and reversibly from pressure of 5 atm to 1 atm at 300 k .The largest mass that can be lifted through a height of 1 metre bt this expansion will be close to

• A. 4000 kg
• B. 4100 kg
• C. 4200 kg
• D. 4300 kg

Answer 1

Answer: (B)

4100 kg

$\text{Given:-}$ $P_1$ = 5 atm

$P_2=$ 1 atm

$T$ = 300 K

$\text{Solution:-}$

Work done in this case is given by

W $=-2.303nRTln\left(\frac{p_1}{p_2}\right)$

Given in the question,

Number of moles, n = 10

R $=8.314J{K}^{-1}mo{l}^{-1}$

T = 300K

Initial pressure $p_1=$ 5 atm

Final pressure $p_2=$ 1 atm

We will now substitute the given values in the equation:

W $=-2.303nRTln\left(\frac{p_1}{p_2}\right)\Rightarrow W=-2.303\times 10\times 8.314\times 300\times ln\frac{5}{1}$

$\Rightarrow$ W $=-2.303\times 10\times 8.314\times 300\times 0.698(Since,ln\frac{5}{1}=0.698)$

$\Rightarrow$ W $=40094.115$ J

Let M be the mass which can be lifted through a height of 1 m

Work done in lifting the mass $=M\times g\times h$

Height = 1 meter (given in the question)

g $=9.8m{s}^{-2}$

W = Mgh

$\Rightarrow$ 20047.057 $=M\times 9.8\times 1$

$\Rightarrow$ M $=\frac{40094\times 115}{9.8\times 1}$ = 4091.236 kg $\approx$ 4100 kg

So, the largest mass which can be lifted through a height of 1 meter by this expansion is 4091.236 kg which is close to 4100 kg.

$\text{Hence the correct option is B}$