Question

How much heat is required to warm \[1.30kg\] of sand from \[{22^ \circ }C\] to  \[{100^ \circ }C\] ?

Answer 1

Hint: Here our duty is to find the heat required to warm the sand. For finding a particular heat released or absorbed when warming a substance , we need to proceed through a specific formula which is given below in the formula used which is the equation for heat capacity. To follow the equation we should know the specific heat capacity of sand. Actually specific heat capacity \[{C_s}\] determines how hard or easy it is to heat up a substance. It will be different for different substances.

Complete answer:

Actually here we should know what heat capacity is before moving to a solution. Heat capacity determines the amount of heat which is required to warm a substance . The particular equation for heat capacity is mentioned above in the formula used.

Next, we shall move onto the solution.

From the equation in the formula used, we actually know the mass as given in the question which is  \[1.30kg\]. But here we need to convert it to grams since specific heat capacities are denoted in units of grams. Therefore the mass, \[m = 1.30kg = 1300g\]

Next, we have to look into \[{C_s}\] which is the specific heat capacity of sand that  should be known to us by referring to various sources and the value is \[0.835\]  . For sand , here we actually write \[{C_s}\]as following,

 \[{C_s} = 0.835 \times \dfrac{J}{{g \times {}^ \circ C}}\]

Next,  we have to look at \[\Delta T\] on the equation, which is actually the temperature difference between final temperature and initial temperature. Here,  \[\Delta T\] is as follows,

 \[\Delta T = {T_f} - {T_i} = 100 - 30 = {70^ \circ }C\]

Next , our duty is to substitute the above values in the top equation as mentioned in the formula used.

\[q = m \times {C_s} \times \Delta T\]

\[q = 1300 \times 0.835 \times 70\]

\[ q= 75985J\]

We know the temperature difference we find above has only one significant figure and therefore we need to round this final answer to one significant figure also .  So , the final answer will be as follows,

\[q = 76000J\]

Hence, the heat required to warm \[1.30kg\] of sand from \[{22^ \circ }C\] to  \[{100^ \circ }C\] is \[76000J\].

Note: Here,  as in this particular question there will be a great chance of getting confused between heat capacity and specific heat capacity. Actually both are different as heat capacity will be greatly varied according to temperature and other factors whereas specific heat capacity is fixed for a particular substance  which varies from substance to substance. We can look up the specific heat capacity of different substances from textbooks , the internet or any other source. We also need to be concerned in converting from kilograms to grams of mass given as it is very important since specific heat capacities are in units of grams.