If the pressure of a gas contained in a closed vessel is increased by 0.4 % when heated by 1 K, its initial temperature must be:

Question

If the pressure of a gas contained in a closed vessel is increased by 0.4 % when heated by 1 K, its initial temperature must be: (A) 250 K (B) 250° C (C) 25°C (D) 25 K

Tardigrade Admin · Accepted Answer

Let initial temperature and pressure be T1 and P1 P2=(P1+(0.4/100) P1) T2=(T2+1) (P1/P2)=(T1/T2) ⇒ (100/100.4)=(T1/(T1+1)) T1=250 K

Q. If the pressure of a gas contained in a closed vessel is increased by $0.4%$ when heated by $1 K$ , its initial temperature must be:

$250 K$

$25 0^{\circ} C$

$2 5^{\circ} C$

$25 K$

Let initial temperature and pressure be $T_{1}$ and $P_{1}$
$P_{2} = (P_{1} + \frac{0.4}{100} P_{1}) T_{2} = (T_{2} + 1)$
$\frac{P _{1}}{P _{2}} = \frac{T _{1}}{T _{2}}$
$\Rightarrow \frac{100}{100.4} = \frac{T _{1}}{( T _{1} + 1 )} T_{1} = 250 K$

Q. If the pressure of a gas contained in a closed vessel is increased by 0.4% when heated by 1K, its initial temperature must be:

250K

250∘C

25∘C

25K