The aluminum block is initially at a temperature of 300 K. It is then brought into contact with 1 mole of gas particles at a temperature of 400 K and constant volume. After some time, the block and the gas thermalize to a common final temperature of 362 K. Of which of the following substances could the gas be composed? a. NH3 b. H2 c. Ar

Completed Question:

The heat capacity of the block of aluminum is 15J/k at 300 K.

Answer:

b. H2

Explanation:

When the block of aluminum is into contact with the gas, they exchange heat until they both achieve thermal equilibrium. If the system is isolated, the heat lost by the gas plus the heat gained by the block must be 0. The gas lost heat because it's hotter than the block.

Qb + Qg = 0

Qb is the heat of the aluminum block and Qg of the gas. The heat is the specific heat multiplied by the change in temperature (final - initial). In the case of the gas, the specific heat (c) must be multiplied by n = 1 mol.

15 * (362 - 300) + 1*c * (362 - 400) = 0

930 - 38c = 0

38c = 930

c = 24.47 J/mol. K

The specific molar heat of the substances given can be found at a thermodinamic table:

cNH3 = 35.06 J/mol. K

cH2 = 28.874 J/mol. K

cAr = 20.786 J/mol. K

So, the closest substance is H2.