The specific heat capacity of a metal is given as 0.745 J/ degree Celcius.What mass of the metal must be heated to 95 degree Celcius in order to be used to warm 2.548 L of water from 18.1 degree Celcius to 22.5 degree Celcius ?
I'm so confused I don't even know where to start
I know that Q= m•s•delta T
I'm thinking to rearrange the equation to
m=q/s•Delta T
I don't know I think what's really throwing me off is the 95degree Celcius
Note the correct spelling of celsius.
You have half of it but not the other half. The metal is heated to 95 C then placed in the water. Then heat lost by the metal + heat gained by the water = 0
heat lost by metal is
q = mass metal x specific heat metal x (Tfinal-Tinitial)
heat gained by the water is
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Set the sum of these to zero and you have it.
[mass metal x specific heat metal x Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
[mass metal x 0.745 x (22.5-95)] + [2548 x 4.184 x (22.5-18.1)] = 0
Only one unknown.
To solve this problem, you can use the equation Q = m * s * ΔT, where Q is the heat transferred, m is the mass, s is the specific heat capacity, and ΔT is the temperature change.
Let's break down the problem into smaller steps:
Step 1: Calculate the heat transferred to the water.
Using Q = m * s * ΔT, we have:
Q_water = m_water * s_water * ΔT_water
Given:
s_water = specific heat capacity of water = 4.18 J/g°C
ΔT_water = temperature change of water = (22.5°C - 18.1°C) = 4.4°C
V_water = volume of water = 2.548 L = 2548 mL
We need to convert mL to grams (g):
1 mL of water is approximately equal to 1 g.
m_water = V_water = 2548 g
Substituting the given values:
Q_water = (2548 g) * (4.18 J/g°C) * (4.4°C)
Step 2: Calculate the heat transferred to the metal.
Using Q = m * s * ΔT, we have:
Q_metal = m_metal * s_metal * ΔT_metal
Given:
s_metal = specific heat capacity of the metal = 0.745 J/°C
ΔT_metal = temperature change of the metal = (95°C - 0°C) = 95°C
Now we have to find the mass of the metal (m_metal) required to transfer the same amount of heat as to the water.
Substituting the given values:
Q_metal = m_metal * (0.745 J/°C) * (95°C)
Step 3: Equate the heats transferred to find the mass of the metal.
Since the heat transferred to the water (Q_water) is equal to the heat transferred to the metal (Q_metal), we can set up the equation:
Q_water = Q_metal
(m_water * s_water * ΔT_water) = (m_metal * s_metal * ΔT_metal)
Substituting the calculated values:
(2548 g) * (4.18 J/g°C) * (4.4°C) = m_metal * (0.745 J/°C) * (95°C)
Now you can solve this equation for m_metal.
m_metal = [(2548 g) * (4.18 J/g°C) * (4.4°C)] / [(0.745 J/°C) * (95°C)]
m_metal ≈ ______ (You can complete the calculation to get the mass of the metal.)
To solve this problem, we can divide it into two parts: heating the metal and warming the water. Let's break down the steps:
1. Calculate the heat energy required to heat the metal:
- Start with the formula Q = m * s * ΔT, where Q is the heat energy, m is the mass of the metal, s is the specific heat capacity, and ΔT is the change in temperature.
- Rearrange the formula to solve for mass: m = Q / (s * ΔT).
- Plug in the given values:
- Q = Unknown
- s = 0.745 J/g°C (convert to J/°C by using the given specific heat capacity of the metal)
- ΔT = (95°C - assuming the initial temperature of the metal is 0°C) = 95°C.
- Calculate the mass of the metal required to reach 95°C.
2. Calculate the heat energy required to warm the water:
- Use the formula Q = m * s * ΔT, where Q is the heat energy, m is the mass of the water, s is the specific heat capacity of water (4.184 J/g°C), and ΔT is the change in temperature.
- Rearrange the formula to solve for mass: m = Q / (s * ΔT).
- Plug in the given values:
- Q = Unknown
- s (specific heat capacity of water) = 4.184 J/g°C (given)
- ΔT = (22.5°C - 18.1°C) = 4.4°C (conversion not required as both temperatures are in °C).
- Calculate the mass of water required to warm it to 22.5°C.
3. Balance the equation to find the mass of the metal required to heat the water:
- Since the heat energy gained by the water is equal to the heat energy lost by the metal, equate the two equations from steps 1 and 2.
- Q (water) = Q (metal).
- Equate the two equations and solve for the unknown.
Let's calculate the mass of the metal and the mass of water required step-by-step.