## Book: HC Verma - Concepts of Physics Part 2

### Chapter: 27. Specific Heat Capacities of Gases

#### Subject: Physics - Class 12th

##### Q. No. 3 of Exercises

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3
##### Figure shows a cylindrical container containing oxygen (γ = 1.4) and closed by a 50 kg frictionless piston. The area of cross section is 100 cm2, atmospheric pressure is 100 kPa and g is 10 ms–2. The cylinder is slowly heated for some time. Find the amount of heat supplied to the gas if the piston moves out through a distance of 20 cm.

Given:

Mass of piston(m) = 50 kg

Area(A) = 100 cm2 = (100x10-4)m2 (since 1m = 100 cm)

Acceleration due to gravity, g = 10 ms-2

Atmospheric pressure = 100 kPa

Distance through which it moves = 20 cm

γ = 1.4

Formula used:

Therefore, pressure exerted by piston = =

= ((50x10)/(100x10-4)) Pa

= 50,000 Pa

Atmospheric pressure = 100 kPa = 1,00,000 Pa.

Therefore, Total pressure(P) = (50,000 + 1,00,000)Pa

=1,50,000Pa

Work done = Pressure x change in volume = P x dV

dV(change in volume) = distance moved by piston x Area

= (20cm x 100cm2)

= 2,000 cm3 = 2,000 x 10-6 m3 = 2 x 10-3 m3

Therefore, Work = (1,50,000 x 2 x 10-3) J = 300 J

Work done, W= P∆V =n R dT

We get,

Now, We calculate Q:

dQ= nCpdt =

Given: γ = 1.4 = . Also,. Solving these two equations, we get Cp = 7R/2, Cv = 5R/2.

Hence, dQ = = 1050 J.

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