A 1.3- block of ice is initially at a temperature of -3.5. If 6.6×105 of heat are added to the ice, what is the final temperature of the system?
Find the amount of ice, if any, that remains.
Suppose the amount of heat added to the ice block is doubled. By what factor must the mass of the ice be increased if the system is to have the same final temperature?
how would i go about trying to do this question(s)? help please.
heat transfer is what the problem is...
you need the specfic heat of water (how water reacts to the increase of heat) or dw(t)/dh (change of water temp with respect to heat added) etc etc its calorie/gram °C = 4.186 joule/gram °C make sure the units are the same and find out how much ice gets above 32 or 0 degrees depending on the units and melts
To solve this question, you can use the formula:
Q = m * c * ΔT
Where:
Q = heat added or removed
m = mass of the substance (in this case, ice)
c = specific heat capacity of the substance
ΔT = change in temperature
1) Finding the final temperature:
Since the ice block is initially at -3.5°C and heat is added, the final temperature will depend on the amount of heat added. Given that 6.6×10^5 J of heat is added, we can find the final temperature using the formula.
Q = m * c * ΔT
6.6×10^5 = 1.3 * c * ΔT
We need the specific heat capacity, c, of ice. The specific heat capacity of ice is approximately 2.09 J/g·°C.
Rearranging the equation, we have:
ΔT = Q / (m * c)
= 6.6×10^5 / (1.3 * 2.09)
Calculate the value of ΔT to find the final temperature.
2) Finding the amount of ice remaining:
To find the amount of ice that remains after the heat is added, we need to determine if the heat added is enough to completely melt the ice. The heat needed to melt ice completely without increasing its temperature is given by:
Q = m * L_f
Where L_f is the latent heat of fusion for ice, which is 334 J/g.
If the heat added, Q, is greater than or equal to the heat required to melt the ice, then all of the ice will be melted and there will be no ice remaining. Otherwise, the remaining ice mass can be found using:
m_remaining = m_initial - (Q / L_f)
3) Doubling the heat added and increasing the ice mass:
If the amount of heat added is doubled, and we want to maintain the same final temperature, we need to determine how much the mass of the ice should be increased.
Since Q = m * c * ΔT, if the heat, Q, is doubled, we need to find the new mass, m_new, such that:
2Q = m_new * c * ΔT
Rearranging the equation, we get:
m_new = (2Q) / (c * ΔT)
Calculate the value of m_new by substituting the 2Q, c, and ΔT with the appropriate values.
By following these steps, you should be able to solve the given question.
To answer these questions, you need to understand the concepts of heat transfer and specific heat capacity.
1. Finding the final temperature and the remaining amount of ice:
To find the final temperature, use the equation:
Q = mcΔT
where Q is the heat added, m is the mass of the substance (in this case, the ice), c is the specific heat capacity of the substance, and ΔT is the change in temperature.
Since we are given the heat added (Q = 6.6×105), the initial temperature (-3.5), and the specific heat capacity of ice (c = 2.09 J/g·°C), we can rearrange the equation to solve for the change in temperature:
ΔT = Q / (mc)
Substituting the given values, we have:
ΔT = (6.6×105) / (1.3 × 2.09)
Compute this value to find the change in temperature.
To find the final temperature, add the change in temperature to the initial temperature:
Final Temperature = -3.5 + ΔT
To find the remaining amount of ice, you need to check if any ice melted during the heating process. If the final temperature is above the melting point of ice (0°C), it means some ice melted. However, if the final temperature is below the melting point of ice, then all the ice remained solid.
2. Doubling the heat added and finding the increased mass of ice:
To determine the increased mass of ice when the heat added is doubled while maintaining the same final temperature, you can use the formula:
Q = mcΔT
Since we want to double Q, we can rewrite the equation as:
2Q = m'cΔT
where m' is the new mass of the ice. Rearranging the equation, we find:
m' = (2Q) / (cΔT)
Substituting the known values from the previous calculations, compute the increased mass of ice.
It is important to note that these calculations assume no heat is lost to the surroundings and that the specific heat capacity of ice remains constant with temperature changes.