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Mechanical Properties Of Fluids

Question
CBSEENPH11019773
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Two moles of diatomic gas at NTP is expanded to four times its initial volume under adiabatic conditions. Find the final temperature and pressure of gas.

Solution
For adiabatic process, 
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and   TV to the power of straight gamma minus 1 end exponent space equals space constant        ...(2) 
From (1),     
         space space space straight P subscript 1 straight V subscript 1 to the power of straight gamma space equals space straight P subscript 2 straight V subscript 2 to the power of straight gamma
rightwards double arrow            straight P subscript 2 space equals space straight P subscript 1 open parentheses straight V subscript 1 over straight V subscript 2 close parentheses to the power of straight gamma 
We have,
straight P subscript 1 space equals space 1 space Atm space space and space space space straight V subscript 1 over straight V subscript 2 equals 1 fourth 
Therefore,
straight P subscript 2 equals 1 open parentheses 1 fourth close parentheses to the power of 1.4 end exponent space equals space 0.144 Atm
From (2),
  straight T subscript 1 straight V subscript 1 to the power of straight gamma minus 1 end exponent space equals space straight T subscript 2 straight V subscript 2 to the power of straight gamma minus 1 end exponent 
 rightwards double arrow     straight T subscript 2 space equals space straight T subscript 1 open parentheses straight V subscript 1 over straight V subscript 2 close parentheses to the power of straight gamma minus 1 end exponent 
Given here,
straight T subscript 1 space space equals space 273 straight K space space space space space and space space space space straight V subscript 1 over straight V subscript 2 equals 1 fourth 
straight T subscript 2 space equals space 273 open parentheses 1 fourth close parentheses to the power of 0.4 end exponent space space space space space space equals space 156.8 straight K space space space space space space space equals space minus 116.2 degree straight C         
T2 and P2 is the final temperature and pressure of the gas respectively. 

Some More Questions From Mechanical Properties of Fluids Chapter

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

What is the SI unit of molar specific heat?

Define heat capacity.

What are the units of heat capacity?

Define Dulong and Pettit’s law of specific heat.

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

Do the gases have only one value of specific heat?

What is thermometry?

Define temperature.

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