Question

A slice of pizza has 500 kcal. If we could burn the pizza and use all the heat to warm a 50-L container of cold water, what would be the approximate increase in the temperature of the water? (Note: A liter of cold-water weighs about 1 kg.)

(A) The option, “50°C is false.

(B) The option, “5°Cis false.

(C) The option, “100°C”, is false.

(D) The option, “10°C”, is true.

Short answer

(A) The option, “50°C is false.

(B) The option, “5°Cis false.

(C) The option, “100°C”, is false.

(D) The option, “10°C”, is true.

Step-by-step solution

Specific Heat of Water

The heat amount needed for raising the temperature of water for 1 degree Celsius for one gram is specific heat capacity. It is higher with respect to common substances when compared, due to which there is a major role of water in the regulation of temperature.

Explanation for option ‘(A)’

There will be a temperature change of 50 degrees Celsius for a 10 L water container for a 50 kcal pizza slice.

The formula for heat is\(Q = mc\Delta T\).

\(\begin{aligned}Q &= mc\Delta T\\500000 &= 10000 \times 1 \times \Delta T\\\Delta T &= \frac{{500000}}{{10000}}\end{aligned}\)

\(\Delta T = 50^\circ {\rm{C}}\)

Thus, the heat change will be\(50^\circ {\rm{C}}\),in the given case.

Therefore, the given statement is false.

Explanation for option ‘(B)’

If there is a change of temperature of 10 degrees Celsius for a 100 L water container for a 50 kcal pizza slice, then 5 degrees Celsius will not be the change.

The formula for heat is\(Q = mc\Delta T\).

\(\begin{aligned}Q &= mc\Delta T\\500000 &= 100000 \times 1 \times \Delta T\\\Delta T &= \frac{{500000}}{{100000}}\end{aligned}\)

\(\Delta T = 5^\circ {\rm{C}}\)

Thus, the heat change will be\(5^\circ {\rm{C}}\), in the given case.

Therefore, the given statement is false.

Explanation for option‘(C)’

The temperature change of 100 degrees Celsius will occur if a 5L of the water container is heated by 50 kcal from pizza.

The formula for heat is\(Q = mc\Delta T\).

\(\begin{aligned}Q &= mc\Delta T\\500000 &= 5000 \times 1 \times \Delta T\\\Delta T &= \frac{{500000}}{{5000}}\end{aligned}\)

\(\Delta T = 100^\circ {\rm{C}}\)

Thus, the heat change will be\(100^\circ {\rm{C}}\), in the given case.

Therefore, the given statement is false.

Explanation for option‘(D)’ 

The heat produced Q is given 500,000 calories from the pizza slice. It generates a change of temperature\(\Delta T\)in \(50{\rm{ kilograms}}\) of water container.

The formula for heat is\(Q = mc\Delta T\).

\(\begin{aligned}Q &= mc\Delta T\\500000 &= 50000 \times 1 \times \Delta T\\\Delta T &= \frac{{500000}}{{50000}}\end{aligned}\)

\(\Delta T = 10^\circ {\rm{C}}\)

Thus, the heat change will be\(10^\circ {\rm{C}}\), in the given case.

Therefore, the given statement is true.