If 7.60 kJ of heat is needed to raise the temperature of a sample of metal from 10.°C to 25°C, how many kilojoules of heat will be required to raise the temperature of the same sample of metal from 35°C to 53°C?

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To find out how many kilojoules of heat will be required to raise the temperature of the same sample of metal from 35°C to 53°C, we need to determine the heat capacity of the metal.

The heat capacity of a substance is the amount of heat required to raise the temperature of a given quantity of the substance by 1 degree Celsius. It is usually denoted by the symbol C and is measured in joules per degree Celsius (J/°C) or kilojoules per degree Celsius (kJ/°C).

In this case, we are given that 7.60 kJ of heat is needed to raise the temperature of the metal from 10°C to 25°C. Therefore, we can calculate the heat capacity of the metal as follows:

Heat capacity = Heat / Temperature change
Heat capacity = 7.60 kJ / (25°C - 10°C)

Calculating the temperature change:
Temperature change = Final temperature - Initial temperature
Temperature change = 25°C - 10°C

Now we can substitute the values into the equation:
Heat capacity = 7.60 kJ / 15°C

Once we have determined the heat capacity, we can use it to find the amount of heat required to raise the temperature from 35°C to 53°C. The temperature change in this case is 53°C - 35°C = 18°C.

Heat = Heat capacity * Temperature change
Heat = (7.60 kJ / 15°C) * 18°C

Calculating the value:
Heat = (7.60 kJ / 15) * 18°C

So, to find the number of kilojoules of heat required to raise the temperature of the sample of metal from 35°C to 53°C, we use the formula: (7.60 kJ / 15) * 18°C.