Question

PuO2 has a density of 11.5 gcm-3 and a specific heat capacity of 330 J kg-1 K-1
. A fresh sample (i.e. one that has not decayed) of PuO2 produces 0.540 kW kg-1 of heat due to internal radioactive decay*. For this question we will consider a 1 cm^3 block of PuO2.

a) How much heat does a fresh 1 cm^3 block of PuO2 produce?

A fresh 1 cm^3 block sitting on the bench in the lab glows red hot at 700 K as it looses heat to
its environment.

b) If we place the block, initially at 700K, in a very well insulated container, its temperature will
start to rise. How long does it take for the block to reach 1000 K?

c) PuO2 melts at 2673 K and its latent heat of fusion is 245 kJ kg-1. If we place our block in a well insulated and heat resistant container when it is at 700 K, then how long is it before the whole block is melted?

Answer 1

Answer on Question #42233-Physics-Molecular Physics-Thermodynamics

PuO2 has a density of 11.5 gcm-3 and a specific heat capacity of 330 J kg-1 K-1. A fresh sample (i.e. one that has not decayed) of PuO2 produces 0.540 kW kg-1 of heat due to internal radioactive decay*. For this question we will consider a 1 cm^3 block of PuO2.

a) How much heat does a fresh 1 cm^3 block of PuO2 produce?

A fresh 1 cm^3 block sitting on the bench in the lab glows red hot at 700 K as it looses heat to its environment.

Answer

$$P = m \cdot \frac {d P}{d m} = \rho \cdot V \cdot \frac {d P}{d m} = 1 1. 5 \frac {g}{c m ^ {3}} \cdot 1 \mathrm {c m} ^ {3} \cdot 0. 5 4 0 \frac {\mathrm {k W}}{\mathrm {k g}} = 6. 2 1 \mathrm {W}.$$

b) If we place the block, initially at 700K, in a very well insulated container, its temperature will start to rise. How long does it take for the block to reach 1000 K?

Answer

$$P \Delta t = \Delta Q = c m \Delta T \rightarrow \Delta t = \frac {c m \Delta T}{P} = \frac {\frac {c \Delta T}{d P}}{d m} = \frac {3 3 0 \frac {\mathrm {J}}{\mathrm {k g K}} \cdot (1 0 0 0 \mathrm {K} - 7 0 0 \mathrm {K})}{0 . 5 4 0 \frac {\mathrm {k W}}{\mathrm {k g}}} = 1 8 3 \mathrm {s}.$$

c) PuO2 melts at 2673 K and its latent heat of fusion is 245 kJ kg-1. If we place our block in a well insulated and heat resistant container when it is at 700 K, then how long is it before the whole block is melted?

Answer

$$\begin{array}{l} P \Delta t = c m \Delta T + q m \rightarrow \Delta t = \frac {c m \Delta T + q m}{P} = \frac {c \Delta T + q}{\frac {d P}{d m}} = \frac {3 3 0 \frac {\mathrm {J}}{\mathrm {k g K}} \cdot (2 6 7 3 \mathrm {K} - 7 0 0 \mathrm {K}) + 2 4 5 \frac {\mathrm {k J}}{\mathrm {k g}}}{0 . 5 4 0 \frac {\mathrm {k W}}{\mathrm {k g}}} \\ = 1. 6 6 \cdot 1 0 ^ {3} s. \\ \end{array}$$

http://www.AssignmentExpert.com/