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1.0molof a monatomic gas interacts thermally with 1.0mol of an elemental solid. The gas temperature decreases by 50oC at constant volume. What is the temperature change of the solid?

Short Answer

Expert verified

The temperature change the solid inΔTsolid=25C

Step by step solution

01

Step :1 Introduction 

In the microsystem, the potential energy between bonds is zero, and the kinetic energy of a monatomic gas is translational kinetic energy.. If the temperature changes by ΔT, then the thermal energy for monatomic gas changes by equation (20.34)in the form

ΔEthgas=32nRΔTgas

Where nis the number of moles and Ris the universal gas constant.

02

Step :2 Explanation 

If the temperature changes by T, then the thermal energy for solid changes by equation (20.34)in the form

ΔEthsolid=3nRΔTsolid

When the gas interacts thermally with the solid, they reach the thermal equilibrium after time, so we can get an expression for Tsolidwhen the number of moles is the same

ΔEthgas=ΔEthsolid

32nRΔTgas=3nRΔTsolid

ΔTsolid=ΔTgas2

03

Step : 3 Values in equation 

Now, we plug the values for Tgasinto equation (3) to get Tsolid

ΔTsolid=ΔTgas2

=50C2

=25C

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