How much heat is required to warm 1.60 kg of sand from 22°C to 100°C?

Question

Wyatt Atkins · Accepted Answer

The energy required to heat the sand by #78^@"C"# is #~~##"36000 J"#.

The specific heat capacity for sand, #c#, is #"0.290 J/g"^@"C"#. https://tutor.hix.ai The equation for determining the heat required to increase the temperature of the sand is #Q=cmDeltaT#, where #Q# is heat energy in Joules, #m# is mass in grams, #c# is specific heat capacity, and #Delta T# is the change in temperature, #(T_"final"-T_"initial")#. #Delta T=(100^@"C")-(22^@"C")=78^@"C"# Mass of sand in grams: #1.60cancel"kg"xx(1000"g")/(1cancel"kg")="1600 g"# Substitute the given values into the equation. #Q=(0.290"J/g"^@"C")xx(1600"g")xx(78^@"C")="36000 J"# (rounded to two significant figures)

Axel Alvarado · Answer

undefined The amount of heat required to warm 1.60 kg of sand from 22°C to 100°C is 198,720 joules.

Natalie Anton · Answer

undefined To calculate the heat required to warm 1.60 kg of sand from 22°C to 100°C, you would use the formula:

$$ Q = mc\Delta T $$

Where:
- $ Q $ is the heat (in joules) required,
- $ m $ is the mass of the sand (in kilograms),
- $ c $ is the specific heat capacity of the material (in joules per kilogram per degree Celsius), and
- $ \Delta T $ is the change in temperature (in degrees Celsius).

First, you would need to find the specific heat capacity of sand. The specific heat capacity of sand varies depending on factors such as its composition and moisture content. However, a common approximation for the specific heat capacity of sand is around 0.84 J/g°C.

Since the specific heat capacity is typically given in joules per gram per degree Celsius, you would need to convert the mass of the sand from kilograms to grams.

Next, you would calculate the change in temperature ($ \Delta T $) by subtracting the initial temperature from the final temperature.

Finally, you would use the formula to find the heat required (in joules) to warm the sand from 22°C to 100°C.