Question

An ideal gas mixture filled inside a balloon expands according to the relation pv 2/3 = constant. the temperature inside the balloon is

Answer 1

I think it would be 40 degree

Answer 2

Temperature increases with increase in volume

Explanation:

Given that a balloon is filled with an ideal gas mixture and expands according to the relation PV^2/3 = constant.  

So PV^(2/3) = constant -------------------- (1)

where P is pressure and V is volume.

As per the ideal gas law, we have PV = RT

where P is pressure, V is volume, T is temperature and R is the ideal gas constant.

So P = RT / V -------------------- (2)

Substituting (2) in (1), we get:

(RT / V) * V^2/3 = constant

RT*V^(-1/3) = constant

Since R is constant, we conclude that T α V^(1/3).

Temperature is directly proportional to volume. So with the increase in volume, temperature of the gas inside the balloon increases.