MCQ
If the pressure of an ideal gas contained in a closed vessel is increased by $0.5\%,$ the increase in temperature is $2K.$ The initial temperature of the gas is ...... $^oC$
- A$27$
- ✓$127$
- C$300$
- D$400$
✓
Answer
Correct option: B.
$127$
b
$P \propto T$ $\Rightarrow$ $\frac{{{P_1}}}{{{P_2}}} = \frac{{{T_1}}}{{{T_2}}}$
$P \propto T$ $\Rightarrow$ $\frac{{{P_1}}}{{{P_2}}} = \frac{{{T_1}}}{{{T_2}}}$
$\Rightarrow$ $\frac{P}{{P + \frac{{0.5}}{{100}}P}} = \frac{T}{{T + 2}}$
$\Rightarrow$ $\frac{{200}}{{201}} = \frac{T}{{T + 2}}$
$\Rightarrow$ $T = 400 \,K = 127°C$
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