Answer:

The final temperature of the metals will be 384.97 K

Explanation:

For the gold;

mass = 1.3 kg

temperature = 300 K

specific heat =  126 J/kg-K

For the copper;

mass = 2.4 kg

temperature = 400 K

specific heat = 386 J/kg-K

Firstly, we will have to calculate for the thermal energy possessed by each of the metal.

The heat possessed by a body =  mcT

Where,

m is the mass of the body

c is the specific heat of the body, and

T is the temperature of the body at that instance

so we calculate for the thermal energy of the gold and the copper below

For gold;

heat energy = mcT = 1.3 x 126 x 300 = 49140 J

For copper;

heat energy = mcT = 2.4 x 386 x 400 = 370560 J

When the two metal come in thermal contact, this heat is evenly distributed between them.

The total heat energy = 49140 J + 370560 J = 419700 J

At thermal equilibrium, the two metals will be at the same temperature, to get this temperature, we equate the total thermal energy to the heat energy that will be possessed by the metals at equilibrium.

419700 = (1.3 x 126 x T) + (2.4 x 386 x T) = 163.8T + 926.4T

419700 = 1090.2T

T = 419700/1090.2 = 384.97 K

The final temperature of the metals will be 384.97 K

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