A certain monatomic gas inside a cylinder is at a temperature of 22°C. It takes 353 J of work done on the gas to compress it and increase the temperature to 145°C. If there are originally 8.2 moles of gas inside the cylinder, calculate the quantity of heat flowing into or out of the gas. (Indicate the direction with the sign of your answer. Let “into the gas” be positive, and “out of the gas” be negative.)
Question
Answer:
[tex]Q=1.22\times 10^{4}\ J.[/tex]
Explanation:
Given :
Temperature of gas , [tex]T=22^o\ C =295\ K.[/tex]
Work done on the gas to compress it , [tex]W = -353 \ J.[/tex]
Final temperature , [tex]T_f=145^o\ C= 418\ K.[/tex]
No of moles , n = 8.2 moles.
We know, by first law of thermodynamics ,
[tex]Q=\Delta U+W\\\\Q=nC_v\Delta T+W[/tex]
( The gas is mono atomic so , [tex]C_v=\dfrac{3}{2}R[/tex] Here R is universal gas constant [tex]8.314\ J\ K^{-1}\ mol^{-1}[/tex])
Putting all values in above equation
We get ,
[tex]Q=(8.2 \times \dfrac{3}{2}\times 8.314 \times 123)+(-353)\\\\Q=12225\ J=1.22\times 10^{4}\ J.[/tex]
Since, Q is positive . Therefore , heat is flowing inside the cylinder.
Hence , this is the required solution.