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### Thermodynamics Numerical

1.An ideal diatomic gas is enclosed in an insulated chamber at temperature 300K. The chamber is closed by a freely movable massless piston, whose initial height from the base is 1m. Now thegas is heated such that its temperature becomes 400 K at constant pressure. Find the new height of the piston from the base.If the gas is compressed to initial position such that no exchangeof heat takes place, find the final temperature of the gas.

2.A cylinder of mass 1 kg is given heat of 20000J at atmospheric pressure. If initially temperature of
cylinder is 200C, find
(a) final temperature of the cylinder.
(b) work done by the cylinder.
(c) change in internal energy of the cylinder.
(Given that Specific heat of cylinder= 400 J kg-1 0C–1, Coefficient of volume expansion
= 9 × 10-5 °C-1, Atmospheric pressure = 105 N/m2 and Density of cylinder = 9000 kg/m3)

3.A gas container has a walls that can bear maximum pressure of 2.2*106 pa.The container contains gas at 4*105 pa and 350K.If the container is steadly heated then neglecting change in volume .Calculate the temperarture at which container will break?

4.A vessel of volume V=20L contains a mixture of hydrogen and helium at T=20° C and Pressue P=2.0 atm.The mass of the mixture is equal to m=5g.Find the ratio of the mass of the hydrgen to that mass of the helium in the mixture Given R=.082 L.atm.mol-1.K-1

5.The first law of thermodynamics dU=dQ-dW,indicates that when a system goes from its intial state to a final state
a. dU is same for every path
b. dQ is same for evry path
c dQ+dW is same for every path
d dQ-2dW is same for every path