Use the worked example above to help you solve this problem. Suppose a system of

Question

Use the worked example above to help you solve this problem. Suppose a system of monatomic ideal gas at 1.50 x 105 Pa and an initial temperature of 293 K slowly expands at constant pressure from a volume of 1.24 L to 2.50 L. (a) Find the work done on the environment. (b) Find the change in internal energy of the gas. (c) Use the First Law of Thermodynamics to obtain the thermal energy absorbed by the gas during the process. (d) Use the molar heat capacity at constant pressure to find the thermal energy absorbed. (e) How would the answers change for a diatomic ideal gas? EXERCISE HINTS: GETTING STARTED I I'M STUCK! Suppose an ideal monatomic gas at an initial temperature of 475 K is compressed from 3.05 L to 1.85 L while its pressure remains constant at 1.01 × 105 Pa. (a) Find the work done on the gas. (b) Find the change in internal energy. (c) Find the energy transferred by heat, 2.

Explanation / Answer

a) Workdone = P*(V2 - V1)

= 1.5*10^5*(2.5 - 1.24)*10^-3

= 189 J

b) change in internal energy = (3/2)*n*R*(T2 -T1)

= (3/2)*P*(V2 - V1)

= (3/2)*1.5*10^5*(2.5 - 1.24)*10^-3

= 283.5 J

c) using, Q = W + delta_U

= 189 + 283.5

= 472.5 J

d) we know, for ideal gas, Cp = (5/2)*R

Q = n*Cp*dT

= n*dT*Cp

= P*(V2-V1)/R)*(5/2)*R

= (5/2)*P*(V2-V1)

= (5/2)*1.5*10^5*(2.5 - 1.24)*10^-3

= 472.5 J

e) delta_U = (5/2)*n*R*(T2 -T1)

= (5/2)*P*(V2 - V1)

= (5/2)*1.5*10^5*(2.5 - 1.24)*10^-3

= 472.5 J

using, Q = W + delta_U

= 189 + 472.5

= 661.5 J

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