$$3$$ moles of an ideal monoatomic gas at a temperature of $$27oC$$ are mixed with $$2$$ moles of an ideal monoatomic gas at a temperature $$227oC$$. Determine the equilibrium temperature of the mixture, assuming no loss of energy.

Question

$$3$$ moles of an ideal monoatomic gas at a temperature of $$27oC$$ are mixed with $$2$$  moles of an ideal monoatomic gas at a temperature $$227oC$$. Determine the  equilibrium temperature of the mixture, assuming no loss of energy.

Infinity Learn · Accepted Answer

Energy possessed by the ideal gas which is at $$27oC$$ is $$E1=3$$×internal energy in the form of $$KEE1=3$$×$$32RT=332$$×$$R(273+27)$$  $$=$$ $$2700R2Energy$$ possessed by the ideal gas which is at $$227oC$$ $$isE2=23R2$$×$$(273+227)=1500RIf$$ T be the equilibrium temperature of the mixture, then its energy will be  $$Em=53RT2Since$$, energy remains conserved, $$Em=E1+E25$$  $$3RT2=2700$$  $$R2+1500R$$⇒$$T=380$$ K or $$T=107$$°C

3 moles of an ideal monoatomic gas at a temperature of 27^oC are mixed with 2 moles of an ideal monoatomic gas at a temperature 227^oC. Determine the equilibrium temperature of the mixture, assuming no loss of energy.

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3 moles of an ideal monoatomic gas at a temperature of 27oC are mixed with 2 moles of an ideal monoatomic gas at a temperature 227oC. Determine the equilibrium temperature of the mixture, assuming no loss of energy.

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3 moles of an ideal monoatomic gas at a temperature of 27^oC are mixed with 2 moles of an ideal monoatomic gas at a temperature 227^oC. Determine the equilibrium temperature of the mixture, assuming no loss of energy.