Answer:
(i) To calculate the mass of the sample of sand, we can use the formula:
mass = density * volume
Given that the density of the sand is 1.90 g/cm³ and the volume is 0.050 m³, we need to convert the volume to the same units as density before plugging the values into the formula.
1 m³ = 100 cm * 100 cm * 100 cm = 1,000,000 cm³
So, the volume of the sand in cm³ is 0.050 m³ * 1,000,000 cm³/m³ = 50,000 cm³.
Now we can calculate the mass:
mass = 1.90 g/cm³ * 50,000 cm³ = 95,000 g.
(ii) The thermal capacity of a substance is the product of its mass and specific heat capacity. To calculate the thermal capacity of the sand, we can use the formula:
thermal capacity = mass * specific heat capacity
Using the mass calculated in part (i) (95,000 g) and the specific heat capacity given in the question (1500 J/(kg °C)), we need to convert the mass to kilograms before plugging the values into the formula.
1 kg = 1000 g
So, the mass of the sand in kilograms is 95,000 g * (1 kg/1000 g) = 95 kg.
Now we can calculate the thermal capacity:
thermal capacity = 95 kg * 1500 J/(kg °C) = 142,500 J/°C.
(iii) To calculate the time taken to increase the temperature of the sand from 7.0 °C to 21.0 °C, we can use the formula:
time = energy / power
The energy required to increase the temperature of the sand can be calculated using the formula:
energy = thermal capacity * temperature change
The temperature change is the final temperature minus the initial temperature:
temperature change = 21.0 °C - 7.0 °C = 14.0 °C.
Now we can calculate the energy:
energy = 142,500 J/°C * 14.0 °C = 1,995,000 J.
Finally, we can calculate the time taken:
time = 1,995,000 J / 50 W = 39,900 seconds.
Therefore, it would take approximately 39,900 seconds to increase the temperature of the sand from 7.0 °C to 21.0 °C.
Step-by-step explanation: