A geyser heats water flowing at the rate of 4 litre per minute from `30^(@) "to" 85^(0) C`. If the geyser operates on a gas burner then the amount of heat used per minute is

Options

A. `9.24xx10^(5)J`
B. `6.24xx10^(7)J`
C. `9.24xx10^(7)J`
D. `6.24xx10^(5)J`

Explanation

To solve the problem of calculating the amount of heat used by the geyser per minute, we will follow these steps:

### Step 1: Identify the given data
- Flow rate of water = 4 liters per minute
- Initial temperature (T1) = 30°C
- Final temperature (T2) = 85°C
- Specific heat capacity of water (c) = 4.2 J/g°C

### Step 2: Convert the flow rate from liters to grams
Since the density of water is approximately 1 g/cm³, we can convert liters to grams:
- 1 liter of water = 1000 grams
- Therefore, 4 liters = 4 × 1000 = 4000 grams

### Step 3: Calculate the change in temperature (ΔT)
ΔT = T2 - T1
- ΔT = 85°C - 30°C = 55°C

### Step 4: Use the formula for heat (Q)
The formula to calculate the heat absorbed or released is:
\[ Q = mcΔT \]
Where:
- Q = heat (in joules)
- m = mass (in grams)
- c = specific heat capacity (in J/g°C)
- ΔT = change in temperature (in °C)

### Step 5: Substitute the values into the formula
Substituting the known values:
\[ Q = 4000 \, \text{g} \times 4.2 \, \text{J/g°C} \times 55 \, \text{°C} \]

### Step 6: Calculate the heat
First, calculate:
- \( 4000 \times 4.2 = 16800 \, \text{J/°C} \)

Now, multiply this by the change in temperature:
\[ Q = 16800 \, \text{J/°C} \times 55 \, \text{°C} = 924000 \, \text{J} \]

### Step 7: Convert the heat to scientific notation
\[ 924000 \, \text{J} = 9.24 \times 10^5 \, \text{J} \]

### Conclusion
The amount of heat used per minute by the geyser is \( 9.24 \times 10^5 \, \text{J/min} \).

---