Calculate the total entropy change hat occurs when 2kg of lead at 40 degrees celcius are placed in a very large quantity of water at 10degrees celcius. the specific heat of lead is 0.031 cal/g K).
According to Newton's 3/2 law, the total entropy change that occurs would be calculated by k*(1/2Ke)mv^2+degrees celcius giving you 1.3999898989898989899898
Well, entropy is a bit like the "chaos" or "disorder" in a system, so let's see how we can calculate the total entropy change in this situation.
First, we need to calculate the heat transferred from the lead to the water. The equation for heat transfer is q = mcΔT, where q is the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Therefore, the heat transferred from the lead is:
q = (2 kg) * (0.031 cal/g K) * (10°C - 40°C)
= -2.48 x 10^2 cal
Now, let's consider the entropy change. The equation for entropy change is ΔS = q/T, where ΔS is the entropy change, q is the heat transferred, and T is the temperature in Kelvin.
Since we are given the specific heat in calories and temperature in degrees Celsius, we need to convert them to Kelvin:
Temperature in Kelvin = Temperature in Celsius + 273.15
Initial temperature of lead in Kelvin = 40°C + 273.15 = 313.15 K
Final temperature of water in Kelvin = 10°C + 273.15 = 283.15 K
Now, we can calculate the entropy change:
ΔS = (-2.48 x 10^2 cal) / 313.15 K
= -0.791 cal/K
Well, it seems the entropy change in this situation is negative. That means the system actually becomes more ordered or less chaotic, which is a bit unusual! But hey, when it comes to entropy, sometimes things defy our expectations and make us scratch our heads.
To calculate the total entropy change, we need to consider the entropy change of both lead and water separately.
1. Entropy change of lead:
The entropy change of lead can be calculated using the formula:
ΔS = mcΔT
where ΔS is the entropy change, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Given:
- Mass of lead (m): 2 kg
- Specific heat capacity of lead (c): 0.031 cal/g K
- Change in temperature (ΔT): (10°C - 40°C) = -30°C
Converting mass to grams:
m_lead = 2 kg * 1000 g/kg = 2000 g
Calculating the entropy change of lead:
ΔS_lead = m_lead * c_lead * ΔT_lead
= 2000 g * 0.031 cal/g°C * -30°C
= -1860 cal/°C
2. Entropy change of water:
The entropy change of water can be calculated in a similar manner.
Given:
- Specific heat capacity of water (c_water): 1 cal/g K
Calculating the entropy change of water:
ΔS_water = m_water * c_water * ΔT_water
= m_water * c_water * (initial temperature - final temperature)
= (∞) * 1 cal/g°C * (10°C - 40°C)
= (∞) * -30 cal/°C
= -∞
Note: The entropy change for water is unlimited because we assumed the amount of water is "very large." In reality, the entropy change for water would be finite and negligible compared to the entropy change of lead.
Total entropy change (ΔS_total) = ΔS_lead + ΔS_water
= -1860 cal/°C + (-∞)
= -∞
Therefore, the total entropy change when 2 kg of lead at 40 degrees Celsius are placed in a very large quantity of water at 10 degrees Celsius is -∞.
To calculate the total entropy change that occurs when lead is placed in water, we need to consider both the entropy change of the lead and the entropy change of the water.
The entropy change (ΔS) can be calculated using the formula:
ΔS = m * Cp * ΔT
Where:
ΔS is the entropy change
m is the mass of the substance (in this case, lead)
Cp is the specific heat capacity of the substance
ΔT is the change in temperature
Given:
Mass of lead (m) = 2 kg = 2000 g
Specific heat capacity of lead (Cp) = 0.031 cal/gK
Temperature change of lead (ΔT) = Final temperature - Initial temperature = (10 °C - 40 °C) = -30 °C
Calculating the entropy change of lead:
ΔS_lead = m_lead * Cp_lead * ΔT_lead
= 2000 g * 0.031 cal/gK * (-30 °C)
= -1860 cal/°C
Now let's calculate the entropy change of the water.
Given:
Assuming a very large quantity of water, so the mass is not given.
Specific heat capacity of water (Cp_water) = 1 cal/gK
Temperature change of water (ΔT) = Final temperature - Initial temperature = (10 °C - 40 °C) = -30 °C
Calculating the entropy change of water:
ΔS_water = m_water * Cp_water * ΔT_water
= m_water * 1 cal/gK * (-30 °C)
However, the mass of water is not given. Since we don't have the mass, we cannot calculate the exact entropy change of water.
Therefore, to calculate the total entropy change, we only have the entropy change of the lead:
Total entropy change = entropy change of lead
= -1860 cal/°C
Please note that mass is required to calculate the entropy change of water.