Question

A 0.371 kg sample of tin initially at 96.1 ◦c is dropped into 0.21 kg of water initially at 11.4 ◦c. if the specific heat capacity of tin is 230 j/kg · ◦c, what is the final equilibrium temperature of the tin-water mixture? the specific heat of water is 4186 j/kg · ◦c. answer in units of ◦c.

Answer 1

The final equilibrium temperature of the tin-water mixture is 50.90°C.

Step-by-step explanation:

To find the final equilibrium temperature of the tin-water mixture, we can use the principle of heat transfer. The heat lost by the hot tin sample must be equal to the heat gained by the cold water. The heat lost or gained can be calculated using the specific heat equation:

Q = mcΔT

Where Q is the heat absorbed or released, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

Applying this equation to the situation:

Heat lost by tin = Heat gained by water

(0.371 kg)(230 J/kg·°C)(Tin final - 96.1°C) = (0.21 kg)(4186 J/kg·°C)(Tin final - 11.4°C)

Simplifying and solving for Tin final:

0.371(230)(Tin final - 96.1) = 0.21(4186)(Tin final - 11.4)

0.371(230Tin final - 230(96.1)) = 0.21(4186Tin final - 4186(11.4))

92.63 Tin final - 8457.13 = 880.26 Tin final - 48545.02

787.63 Tin final = 40087.89

Tin final = 50.90°C

Answer 2

The equilibrium temperature of the tin-water mixture is found by setting the heat lost by the tin equal to the heat gained by the water, using the specific heat capacities and the formula for heat transfer, and solving for the equilibrium temperature.

Step-by-step explanation:

The question involves finding the final equilibrium temperature of a tin-water mixture, using principles of heat transfer and specific heat capacities. According to the principle of conservation of energy, the heat lost by the tin will equal the heat gained by the water when they reach equilibrium. We use the formula mcΔT, where m is mass, c is specific heat capacity, and ΔT is the change in temperature.

To find the equilibrium temperature Teq, we set the heat lost by tin equal to the heat gained by water and solve for Teq.

Let mSn = 0.371 kg (mass of tin), cSn = 230 J/kg·°C (specific heat of tin), Ti,Sn = 96.1°C (initial temperature of tin), mH2O = 0.21 kg (mass of water), cH2O = 4186 J/kg·°C (specific heat of water), and Ti,H2O = 11.4°C (initial temperature of water).

The equation for the heat loss/gain is:

mSncSn(Teq - Ti,Sn) = mH2OcH2O(Ti,H2O - Teq)

Solving this equation for Teq:

Teq = [(mSncSnTi,Sn) + (mH2OcH2OTi,H2O)] / [(mSncSn) + (mH2OcH2O)]

After plugging in the given values and solving the equation, we can find the final equilibrium temperature of the mixture.