A tank contains 200 g of water maintained at temperature of 27 ° C. The water is heated to raise its temperature to 100 ° C. The heat energy required is x kJ.
The value of x is
a) 83.6 kJ
b) 61.3 kJ
c) 62.3 kJ
d) 60.2 kJ
e) 63.2 kJ
To find the heat energy required to heat the water, we can use the formula:
Q = mcΔT
Where Q is the heat energy, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
First, we need to find the mass of the water. Since the unit given is grams, we don't need to convert it. So, m = 200 g.
Next, we need to find the change in temperature. Since the initial temperature is 27 °C and the final temperature is 100 °C, we have:
ΔT = (100 °C - 27 °C) = 73 °C
The specific heat capacity of water is approximately 4.18 J/g°C.
Now, we can calculate the heat energy:
Q = mcΔT = (200 g)(4.18 J/g°C)(73 °C)
Note that we need to convert the result from joules to kilojoules (kJ). Since 1 kJ = 1000 J, we have:
Q = (200 g)(4.18 J/g°C)(73 °C) / 1000 J/kJ = 61.364 kJ
Rounded to one decimal place, the answer is 61.3 kJ.
So, the correct answer is b) 61.3 kJ.
is the calulations correct?
Yes, the calculations are correct. The final answer of 61.3 kJ is the correct amount of heat energy required to raise the temperature of 200 g of water from 27 °C to 100 °C.
To find the value of x, we need to calculate the heat energy required to raise the temperature of 200 g of water from 27 °C to 100 °C. The heat energy required can be determined using the formula:
Q = mcΔT
Where Q is the heat energy required, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
The specific heat capacity of water is approximately 4.18 J/g°C, which means that it takes 4.18 joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.
First, let's convert the mass of water from grams to kilograms:
Mass of water = 200 g = 0.2 kg
Next, let's calculate the change in temperature:
ΔT = Final temperature - Initial temperature
ΔT = 100 °C - 27 °C
ΔT = 73 °C
Now, we can calculate the heat energy required:
Q = mcΔT
Q = 0.2 kg * 4.18 J/g°C * 73 °C
Q = 0.2 kg * 4.18 J/(g°C) * 73 °C
Q = 60.892 J
However, the options given for x are in kilojoules (kJ), so we need to convert the value to kilojoules:
60.892 J * (1 kJ/1000 J) = 0.060892 kJ
Therefore, the value of x is approximately 0.060892 kJ, which is closest to the value in option (d), 60.2 kJ.