Question

Calculate the heat required to raise the temperature of 75.1 g of mercury from 31.7 °C to 53.8 °C. The specific heat capacity of mercury is 0.14 J/(g∙ °C).

Answer 1

`Q=232.36J`

Step-by-step explanation:

The heat capacity (C) of a physical system depends on the amount of substance of that system. For a system formed by a single homogeneous substance, it is defined as:

`C=mc(1)`

Here m is the mass of the system and c is the specific heat capacity.

The heat capacity is defined as the ratio between the heat absorbed by the system and the resulting temperature change:

`C=(Q)/(\Delta T)(2)`

We equal (1) and (2) and solve for Q:

`(Q)/(\Delta T)=mc\\Q=mc\Delta T\\Q=mc(T_f-T_i)\\Q=75.1g(0.14(J)/(g^\circ C))(53.8^\circ C-31.7^\circ C)\\Q=232.36J`

Answer 2

232 J

Step-by-step explanation:

Heat gained = mass × specific heat × increase in temperature

q = m C (T − T₀)

Given m = 75.1 g, C = 0.14 J/g/°C, T = 53.8°C, and T₀ = 31.7°C:

q = (75.1 g) (0.14 J/g/°C) (53.8°C − 31.7°C)

q = 232 J