When a gas-filled in a closed vessel is heated through 1 ° C , its pressure increases by 0.4 % . The initial temperature of the gas was

Question

When a gas-filled in a closed vessel is heated through 1 ° C , its pressure increases by 0.4 % . The initial temperature of the gas was (A) 250K (B) 2500K (C) 250° C (D) 25 ° C

Tardigrade Admin · Accepted Answer

p1=p and T1=T ; p2=p+(0.4/100)p=1.004p ;T2=(.T+1.) As (p2/p1)=(T2/T1) ∴ (1.004 p/p)= (T + 1/T)=1+(1/T) Or T=(1/0.004)=250 K

Q. When a gas-filled in a closed vessel is heated through $1^{\circ} C$ , its pressure increases by $0.4%$ . The initial temperature of the gas was

$250 K$

$2500 K$

$25 0^{\circ} C$

$25^{\circ} C$

$p_{1} = p an d T_{1} = T;$
$p_{2} = p + \frac{0.4}{100} p = 1.004 p; T_{2} = (T + 1)$
As $\frac{p _{2}}{p _{1}} = \frac{T _{2}}{T _{1}} ∴ \frac{1.004 p}{p} = \frac{T + 1}{T} = 1 + \frac{1}{T}$
Or $T = \frac{1}{0.004} = 250 K$

Q. When a gas-filled in a closed vessel is heated through 1∘C , its pressure increases by 0.4% . The initial temperature of the gas was

250K

2500K

250∘C

25∘C