Question

The pressur of a gas filled in a closed vessel increases by 0.4℅ when temprature is increased by 1°C. Find the initial temprature of the gas.

Answer 1

This is an impossible question. However, if we assume that the question should have written that the vessel is rigid, then I get an initial temperature of

250 K

.

Well, as usual, when you see pressure, temperature, and "closed vessel" in the same sentence, we assume ideality...

PV=nRT

P

is pressure in

atm

.

V

is volume in

L

.

n

is mols of ideal gas.

R=0.082057 L⋅atm/mol⋅K

is the universal gas constant.

T

is temperature in

K

(as it must be! Why?).

The closed vessel means very little to us; all it says is that the mols of gas are constant. It says nothing about the volume of the vessel being constant, as it could very well be a big fat balloon.

We apparently are given:

P→1.004P

T→T+1

n→n

V→???×V

Substitute to get:

1.004P⋅V=nR(T+1)=nRT+nR

,

where the written variables are all for the initial state and we interpret the question to mean a closed AND rigid vessel. So, we assume that

???=1

.

Note that since

PV=nRT

, we can now write:

1.004nRT=nR(T+1)

Then, divide by

nR

to get:

1.004T=T+1

⇒0.004T=1

⇒T=

10.004

=250 K

which is one of the given answer choices. It doesn't mean the question can't be revised, but that is probably what the question actually meant.