Question

It is found, on heating a gas, its volume increases
by 50% and pressure decreases to 60% of its original
value. If the original temperature was -15 degree
Celcius, find the temperature to which it was heated in
Celcius

Answer 1

Answer:

The RMS speed depends only on the weight of the gas molecules and the temperature of the gas. So if the temperature is fixed, changing the volume has no effect on the speed. It does change the frequency of collisions between the particles, which is what causes the pressure to rise; but that’s only because the molecules are closer together, not because they are going any faster.

As pointed out in an earlier answer, if you compress a gas its temperature will normally rise, because it takes “work” to do it (the force required, times the decrease in volume), and that is usually converted to heat. But if you compress it so slowly that any extra heat is radiated away as fast as it is generated and the temperature remains fixed (as hypothesized), then the RMS speed is unaffected.

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Answer 2

Answer:

Let the original volume (V)=1 and

the original pressure (P)=1 and

the temperature given (T)= −15°C = −15+273=258K

V1 or new volume after heating = original volume +50% of original volume

1 + 1 × 50/100 = 1 + 1/2 = 3/2

Here P1 is the decreased pressure

P 1 = 60%

= 1 x 60 / 100

= 0.6

T1=?

PV/T = P1 V1 / T1

1×1 / 258 = 3/2 × 0.6/T1

T1 = 232.2K

T1 = 232.2−273 = −40.8°C

So, the temperature to which it was heated in Celcius = -40.8°C