Answer to Question #170086 in Physics for Hephzibah chinwendu

Question

What is the quantity of heat that is required to convert 4kg of ice into steam at 100^°c ?

Answer 1

Unfortunately, from the condition of the question we don't know the temperature of ice, so let assume that the temperature of ice is -10°C.

$$Q=Q_1+Q_2+Q_3+Q_4,$$ $$Q=m_ic_i\Delta T+m_iL_f+m_wc_w\Delta T+m_wL_v.$$

Let's find the amount of heat required to convert 4 kg of ice at -10°C to 4 kg of ice at 0°C:

$$Q_1=m_ic_i\Delta T=4\ kg\cdot2100\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot10^{\circ}C=84000\ J.$$

Let's find the amount of heat required to convert 4 kg of ice at 0°C to 4 kg of water at 0°C:

$$Q_2=m_iL_f=4\ kg\cdot3.34\cdot10^5\ \dfrac{J}{kg}=1336000\ J.$$

Let's find the amount of heat required to convert 4 kg of water at 0°C to 4 kg of water at 100°C:

$$Q_3=m_wc_w\Delta T=4\ kg\cdot4180\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot100^{\circ}C=16720000\ J.$$

Let's find the amount of heat required to convert 4 kg of water at 100°C to 4 kg of steam at 100°C:

$$Q_4=m_wL_v=4\ kg\cdot2.264\cdot10^6\ \dfrac{J}{kg}=9056000\ J.$$

Finally, the total amount of the heat required to convert 4 kg of ice at -10°C to steam at 100°C:

$$Q=84000\ J+1336000\ J+16720000\ J+9056000\ J=27196000\ J.$$