Solve -101.325*10^3*5*8.314*300*(1/101.325^3-1/1013.25^3)

$$-101.325 \times { 10 }^{ 3 } \times 5 \times 8.314 \times 300 \times ( \frac{ 1 }{ { 101.325 }^{ 3 } } - \frac{ 1 }{ { 1013.25 }^{ 3 } } )$$

Evaluate

$$-\frac{2214849600}{1825201}\approx -1213.482569865$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$-101.325\times 1000\times 5\times 8.314\times 300\left(\frac{1}{101.325^{3}}-\frac{1}{1013.25^{3}}\right)$$

Multiply -101.325 and 1000 to get -101325.

$$-101325\times 5\times 8.314\times 300\left(\frac{1}{101.325^{3}}-\frac{1}{1013.25^{3}}\right)$$

Multiply -101325 and 5 to get -506625.

$$-506625\times 8.314\times 300\left(\frac{1}{101.325^{3}}-\frac{1}{1013.25^{3}}\right)$$

Multiply -506625 and 8.314 to get -4212080.25.

$$-4212080.25\times 300\left(\frac{1}{101.325^{3}}-\frac{1}{1013.25^{3}}\right)$$

Multiply -4212080.25 and 300 to get -1263624075.

$$-1263624075\left(\frac{1}{101.325^{3}}-\frac{1}{1013.25^{3}}\right)$$

Calculate 101.325 to the power of 3 and get 1040279.013703125.

$$-1263624075\left(\frac{1}{1040279.013703125}-\frac{1}{1013.25^{3}}\right)$$

Expand \frac{1}{1040279.013703125} by multiplying both numerator and the denominator by 1000000000.

$$-1263624075\left(\frac{1000000000}{1040279013703125}-\frac{1}{1013.25^{3}}\right)$$

Reduce the fraction \frac{1000000000}{1040279013703125} to lowest terms by extracting and canceling out 15625.

$$-1263624075\left(\frac{64000}{66577856877}-\frac{1}{1013.25^{3}}\right)$$

Calculate 1013.25 to the power of 3 and get 1040279013.703125.

$$-1263624075\left(\frac{64000}{66577856877}-\frac{1}{1040279013.703125}\right)$$

Expand \frac{1}{1040279013.703125} by multiplying both numerator and the denominator by 1000000.

$$-1263624075\left(\frac{64000}{66577856877}-\frac{1000000}{1040279013703125}\right)$$

Reduce the fraction \frac{1000000}{1040279013703125} to lowest terms by extracting and canceling out 15625.

$$-1263624075\left(\frac{64000}{66577856877}-\frac{64}{66577856877}\right)$$

Since \frac{64000}{66577856877} and \frac{64}{66577856877} have the same denominator, subtract them by subtracting their numerators.

$$-1263624075\times \frac{64000-64}{66577856877}$$

Subtract 64 from 64000 to get 63936.

$$-1263624075\times \frac{63936}{66577856877}$$

Reduce the fraction \frac{63936}{66577856877} to lowest terms by extracting and canceling out 27.

$$-1263624075\times \frac{2368}{2465846551}$$

Express -1263624075\times \frac{2368}{2465846551} as a single fraction.

$$\frac{-1263624075\times 2368}{2465846551}$$

Multiply -1263624075 and 2368 to get -2992261809600.

$$\frac{-2992261809600}{2465846551}$$

Reduce the fraction \frac{-2992261809600}{2465846551} to lowest terms by extracting and canceling out 1351.

$$-\frac{2214849600}{1825201}$$

Factor

$$-\frac{2214849600}{1825201} = -1213\frac{880787}{1825201} = -1213.482569864908$$