Your hot water tank is insulated, but not very well. To...

Your hot water tank is insulated, but not very well. To reduce heat loss, you wrap some old blankets around it. With the water at $81^{\circ} \mathrm{C}$ and the room at $21^{\circ} \mathrm{C},$ a thermometer inserted between the outside of the original tank and your blanket reads $36^{\circ} \mathrm{C} .$ By what factor did the blanket reduce the heat loss?

Key Concepts

Temperature Gradient

The temperature gradient is the difference in temperature across a material that drives heat flow. Understanding the gradient, especially when additional insulation is applied, is key to determining changes in the heat loss rate.

Steady-State Heat Transfer

Steady-state heat transfer assumes that the temperature distribution remains constant over time, meaning the rate of heat entering any part of the system equals the rate of heat leaving. This assumption simplifies analysis by focusing on the balance of thermal resistances and temperature differences.

Thermal Resistance

Thermal resistance quantifies the opposition a material offers to heat flow, similar to electrical resistance in a circuit. It allows us to model how added layers, such as blankets, increase the barrier to heat loss by reducing the rate of heat transfer.

Insulation

Insulation involves using materials with high thermal resistance to reduce the rate of heat loss or gain. It plays a critical role in improving energy efficiency by slowing down the transfer of heat between objects at different temperatures.

Heat Conduction

Heat conduction is the process by which thermal energy is transmitted through a material when there is a temperature gradient. In problems like this, conduction explains how heat moves from the hotter water to the cooler surroundings and how insulating materials affect that transfer.

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