Water can be heated in tightly woven baskets by dropping in hot rocks. The technique is useful for cooking in the absence of metal or pottery vessels. Estimate the size (in liters) of basket needed to hold the rocks and water if 5 L of boiling-hot (100°C) water is required. The water comes from a well at 10°C, and the rocks (granite with a density of 2.7 g cm−3) come from a hot fire at 900°C. Take data from Table 10−1. List the assumptions required to make the estimate.
A)6 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C
(2) the density of the rock is 2.7 g cm−3 at 100°C
(3) the energy created by the rocks are transfered to the water at a constant rate.
(4) heat is lost to the surroundings through the walls of the basket
(5) The rocks decrease in size as a function of temperature
B)6 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C
(2) the density of the rock is 2.7 g cm−3 at 100°C
(3) the specific heat capacities of the water and rock do not change with temperature
(4) no heat is lost to the surroundings through the walls of the basket
(5) no heat is used to warm up the walls of the basket
C)6 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C
(2) the density of the rock is 2.7 g cm−3 at 100°C
(3) the energy created by the rocks are transfered to the water at a constant rate.
(4) no heat is lost to the surroundings through the walls of the basket
(5) no heat is used to warm up the walls of the basket
D)8 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C
(2) the density of the rock is 2.7 g cm−3 at 100°C
(3) the specific heat capacities of the water and rock do not change with temperature
(4) no heat is lost to the surroundings through the walls of the basket
(5) no heat is used to warm up the walls of the basket
E)8 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C
(2) the density of the rock is 2.7 g cm−3 at 100°C
(3) the specific heat capacities of the water and rock do not change with temperature
(4) heat is lost to the surroundings through the walls of the basket
(5) The rocks decrease in size as a function of temperature
F) 8 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C
(2) the density of the rock is 2.7 g cm−3 at 100°C
(3) the energy created by the rocks are transfered to the water at a constant rate.
(4) heat is lost to the surroundings through the walls of the basket
(5) The rocks decrease in size as a function of temperature
B) 6 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C
(2) the density of the rock is 2.7 g cm−3 at 100°C
(3) the specific heat capacities of the water and rock do not change with temperature
(4) no heat is lost to the surroundings through the walls of the basket
(5) no heat is used to warm up the walls of the basket
To estimate the size of the basket needed to hold the rocks and water, we can use the concept of density.
First, let's consider the water. We are given that 5 L of boiling-hot (100°C) water is required. We assume that the density of water remains constant between 10.0°C and 100°C. Using Table 10-1 (which is not provided here), we can look up the density of water at 10.0°C. Let's assume it is 1.00 g/cm³.
Next, let's consider the rocks. We are given that the rocks come from a hot fire at 900°C and have a density of 2.7 g/cm³ at 100°C. We assume that the density of the rocks remains constant at 2.7 g/cm³ during the process.
Now, let's analyze the assumptions for each answer choice:
A) 6 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C → Correct assumption
(2) the density of the rock is 2.7 g/cm³ at 100°C → Correct assumption
(3) the energy created by the rocks are transferred to the water at a constant rate → No information is provided about the energy transfer rate. Incorrect assumption.
(4) heat is lost to the surroundings through the walls of the basket → Correct assumption
(5) The rocks decrease in size as a function of temperature → No information is provided about the change in size. Incorrect assumption.
B) 6 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C → Correct assumption
(2) the density of the rock is 2.7 g/cm³ at 100°C → Correct assumption
(3) the specific heat capacities of the water and rock do not change with temperature → No information is provided about specific heat capacities. Incorrect assumption.
(4) no heat is lost to the surroundings through the walls of the basket → Incorrect assumption. Heat loss is stated in the question.
(5) no heat is used to warm up the walls of the basket → Incorrect assumption. Heat transfer to the walls of the basket is not discussed.
C) 6 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C → Correct assumption
(2) the density of the rock is 2.7 g/cm³ at 100°C → Correct assumption
(3) the energy created by the rocks are transferred to the water at a constant rate → No information is provided about the energy transfer rate. Incorrect assumption.
(4) no heat is lost to the surroundings through the walls of the basket → Incorrect assumption. Heat loss is stated in the question.
(5) no heat is used to warm up the walls of the basket → Incorrect assumption. Heat transfer to the walls of the basket is not discussed.
D) 8 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C → Correct assumption
(2) the density of the rock is 2.7 g/cm³ at 100°C → Correct assumption
(3) the specific heat capacities of the water and rock do not change with temperature → No information is provided about specific heat capacities. Incorrect assumption.
(4) no heat is lost to the surroundings through the walls of the basket → Incorrect assumption. Heat loss is stated in the question.
(5) no heat is used to warm up the walls of the basket → Incorrect assumption. Heat transfer to the walls of the basket is not discussed.
E) 8 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C → Correct assumption
(2) the density of the rock is 2.7 g/cm³ at 100°C → Correct assumption
(3) the specific heat capacities of the water and rock do not change with temperature → No information is provided about specific heat capacities. Incorrect assumption.
(4) heat is lost to the surroundings through the walls of the basket → Correct assumption
(5) The rocks decrease in size as a function of temperature → No information is provided about the change in size. Incorrect assumption.
F) 8 L
Assumptions:
(1) the density of the water does not change between 10.0°C to 100°C → Correct assumption
(2) the density of the rock is 2.7 g/cm³ at 100°C → Correct assumption
(3) the energy created by the rocks are transferred to the water at a constant rate → No information is provided about the energy transfer rate. Incorrect assumption.
(4) heat is lost to the surroundings through the walls of the basket → Correct assumption
(5) The rocks decrease in size as a function of temperature → No information is provided about the change in size. Incorrect assumption.
Based on the analysis, answer choice A) 6 L is the most appropriate selection.