the water in a swimming pool transfers 1.09 x 10^10 J of energy as heat to the cool night air. If the temp of the water, which has a specific heat capacity of 4186 J/kg x °C, decreases by 5.0°C, what is the mass of the water in the pool?
q=mcdeltatemp
m= 1.09E10/c*5
You are given C, solve for mass in kg
190
To find the mass of the water in the pool, we can use the formula:
Q = mcΔT
Where:
Q = energy transferred as heat (J)
m = mass of the water (kg)
c = specific heat capacity of water (J/kg x °C)
ΔT = change in temperature (°C)
Given:
Q = 1.09 × 10^10 J
c = 4186 J/kg x °C
ΔT = -5.0 °C (negative because the temperature is decreasing)
Let's substitute the given values into the formula and solve for the mass, m:
1.09 × 10^10 J = m × 4186 J/kg x °C × -5.0 °C
Divide both sides of the equation by -5.0 °C and 4186 J/kg x °C:
m = (1.09 × 10^10 J) / (4186 J/kg x °C × -5.0 °C)
m ≈ 5202 kg
Therefore, the mass of the water in the pool is approximately 5202 kg.
To find the mass of the water in the pool, we can use the equation:
Q = mcΔT
where:
Q = amount of thermal energy transferred (in this case, 1.09 x 10^10 J)
m = mass of the water
c = specific heat capacity of water (4186 J/kg x °C)
ΔT = change in temperature (in this case, -5.0 °C)
Rearranging the equation to solve for mass (m), we get:
m = Q / (c * ΔT)
Now, let's substitute the given values into the equation:
m = (1.09 x 10^10 J) / (4186 J/kg x °C * -5.0 °C)
Note that we multiplied the change in temperature by -1 since it decreased.
m = (1.09 x 10^10 J) / (-20930 J/kg)
Simplifying further:
m ≈ -5.206 x 10^5 kg
Mass cannot be negative, so we neglect the negative sign and the mass of the water in the pool is approximately 5.206 x 10^5 kg.