Question

How much heat energy (in megajoules) is needed to convert 7 kilograms of ice at –9°C to water at 0°C?

A. 2.13 MJ
B. 2.48 MJ
C. 3.09 MJ
D. 3.26 MJ

Answer 1

How much heat energy (in megajoules) is needed to convert 7 kilograms of ice at –9°C to water at 0°C?

A. 2.13 MJ

B. 2.48 MJ

C. 3.09 MJ

D. 3.26 MJ

The correct answer for this question is B. 2.48

Answer 2

Answer: 2471 kJ

Step-by-step explanation:

The problem can be split into two steps:

1- Calculate the heat energy needed to raise the temperature of the ice from -9 C to 0 C

2- Calculate the heat energy required to melt the ice

Let's solve them separately.

1- The heat energy needed to raise the temperature of the ice from -9 C to 0 C is given by:

`Q=mC_s \Delta T`

where

m=7 kg is the mass of the ice

Cs=2108 J/kgK is the specific heat capacity of ice

`\Delta T=0 C - (-9 C)=9 C` is the temperature gain

Substituting into the formula,

`Q_1=(7 kg)(2108 J/kg C)(9 C)=132,804 J=133 kJ`

2- the heat energy required to melt the ice is given by

`Q = m \lambda_f`

where

m=7 kg is the mass of the ice

`\lambda_f=334 kJ/kg` is the specific latent heat of fusion for ice

Substituting into the formula,

`Q_2 = (7 kg)(334 kJ/kg)=2,338 kJ`

3- So, the total heat energy needed for the entire process is

`Q=Q_1 +Q_2 =133 kJ+2,338 kJ=2,471 kJ`